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Computing the connected components of an undirected graph G = (V,E) on |V| = n vertices and |E| = m edges is a fundamental computational problem. The best known parallel algorithm for the CREW PRAM model runs on O(lg2n) time using n2/lg2n processors [CLC82,HCS79]. For the CRCW PRAM model in which concurrent writing is permitted, the best known algorithm runs in O(lg n) time using almost (n+m)/lg n processors [SV82,CV86,AS87]. Unfortunately, simulating this algorithm on the weaker CREW model increases its running time to O(lg2n) [CDR86, KR90,Vis83]. We present here an efficient and simple algorithm that runs in O(lg 3/2n) time using n+m CREW processors.
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Donald B. Johnson and Panagiotis Metaxas, "Connected Components in O(lg3/2|V|) Parallel Time for the CREW PRAM." Dartmouth Computer Science Technical Report PCS-TR91-160, 1991.
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